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Let ƒ be a 2-cocycle of a finite group G over the multiplicative group of the complex field with trivial action. Schur already knew that the number of irreducible projective characters of G in C for ƒ (or ƒ-characters for short) is less than or equal to the number of conjugacy classes of G. No one seems to have asked whether it is possible to have equality when ƒ is not a coboundary. We show that ... read morethis can indeed happen, give a simple criterion for it, and discuss some examples. First published in Proceedings of Symposia in Pure Mathematics in volume 47.2, published by the American Mathematical Society.read less
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